The precision of quantum sensing could be improved by exploiting quantum
phase transitions, where the physical quantity tends to diverge when the system
is approaching the quantum critical point. This critical enhancement phenomenon
has been applied to the quantum Rabi model in a dynamic framework, showing a
promising sensing enhancement without the complex initial state preparation. In
this work, we find a quantum phase transition in the coupling cavity-mechanical
oscillator system when the coupling strength crosses a critical point,
determined by the effective detuning of cavity and frequency of mechanical
mode. By utilizing this critical phenomenon, we obtain a prominent enhancement
of quantum sensing, such as the position and momentum of the mechanical
oscillator. This result provides an alternative method to enhance the quantum
sensing of some physical quantities, such as mass, charge, and weak force, in a
large mass system